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9-2-1a - 2-1 Part I Polynomials Example polynomial 3x2 2x 1...

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2-1 Part I: Polynomials Example polynomial: 3x 2 - 2x + 1 3 terms: quadratic linear constant leading coeff. 3 x 2 -2 x +1 coefficient of degree of coefficient of quadratic term polynomial linear term leading term : term of highest degree; here it is 3x 2 degree : degree of leading term The tails of the graph of a polynomial: 2-1 Part I p. 1
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Polynomial Tail Principle: for a polynomial, the tails will always go to + or - , AND tail behavior will be dictated by the leading term, as follows: leading coefficient leading term: + - even example: 3x 4 left tail + right tail + picture: example: -3x 4 left tail - right tail - picture: odd example: 3x 3 left tail - right tail + picture: example: -3x 3 left tail + right tail - picture: Summary: even leading term: tails go same direction ( for +, for -) odd leading term: tails go opposite ( ↓↑ for +, ↑↓ for -) Example: f(x) = -7x 2 - 3x 4 + 7 leading term: -3x 4 even : go same direction coeff is -: direction is down ( ↓↓ ) 2-1 Part I p. 2
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